Global gradient estimates for degenerate parabolic equations in nonsmooth domains
Global gradient estimates for degenerate parabolic equations in nonsmooth domains
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DOI：
10.1007/s10231-008-0079-0
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发表时间：
2009-04-01
影响因子：
1
通讯作者：
Parviainen, Mikko
中科院分区：
文献类型：
--
作者：
Parviainen, Mikko
本文研究退化非线性抛物型偏微分方程解的整体正则性。我们的目的是证明如果区域的补集满足容量密度条件并且边值足够光滑，则弱解属于比先验假设更高的Soblev空间。此外，我们还给出了梯度的可积性估计。所得结果也推广到抛物型方程组。更高的可积性估计在几个应用中提供了一个有用的工具。
This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates for the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful tool in several applications.